Latest developments in 3D analysis of geomaterials by Morpho+

At the Centre for X-ray Tomography of the Ghent University (Belgium) (www.ugct.ugent.be) besides hardware development for high-resolution X-ray CT scanners, a lot of progress is being made in the field of 3D analysis of the scanned samples. Morpho+ is a flexible 3D analysis software which provides the necessary petrophysical parameters of the scanned samples in 3D. Although Morpho+ was originally designed to provide any kind of 3D parameter, it contains some specific features especially designed for the analysis of geomaterial properties like porosity, partial porosity, pore-size distribution, grain size, grain orientation and surface determination. Additionally, the results of the 3D analysis can be visualized which enables to understand and interpret the analysis results in a straightforward way. The complementarities between high-quality X-ray CT images and flexible 3D software are opening up new gateways in the study of geomaterials

On Using Physical Analogies for Feature and Shape Extraction in Computer Vision

There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but impeded by speed of computation. We have developed new ways to extract features based on notional use of physical paradigms, with parameterisation that is more familiar to a scientifically-trained user, aiming to make best use of computational resource. We describe how analogies based on gravitational force can be used for low-level analysis, whilst analogies of water flow and heat can be deployed to achieve high-level smooth shape detection. These new approaches to arbitrary shape extraction are compared with standard state-of-art approaches by curve evolution. There is no comparator operator to our use of gravitational force. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision

Determining maximum k-width-connectivity on meshes

AbstractLet I be a n × n binary image stored in a n × n mesh of processors with one pixel per processor. Image I is k-width-connected if, informally, between any pair of 1-pixels there exists a path of width k (composed of 1-pixels only). We consider the problem of determining the largest integer k such that I is k-width-connected, and present an optimal O(n) time algorithm for the mesh architecture

Fractal Topological Analysis for 2D Binary Digital Images

Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological model of them, called Homological Spanning Forest (HSF, for short). Defined at interpixel level, this set of two trees allows to topologically describe the (black and white) connected component distribution within the image with regards to the relationship “to be surrounded by”. This distribution is condensed into a rooted tree, such that its nodes are connected components determined by some special sub-trees of the previous HSF and the levels of the tree specify the degree of nesting of each connected component. We ask for topological auto-similarity by comparing this topological description of the whole image with a regular rooted tree pattern. Such an analysis can be used to directly quantify some characteristics of biomedical images (e.g. cells samples or clinical images) that are not so noticeable when using geometrical approaches.Ministerio de Economía y Competitividad TEC2016-77785-PMinisterio de Economía y Competitividad MTM2016-81030-

AUTOMATIC OPTICAL INSPECTION-BASED PCB FAULT DETECTION USING IMAGE PROCESSING

Increased Printed Circuit Board (PCB) route complexity and density combined with the growing demand for low-scale rapid prototyping has increased the desire for Automated Optical Inspection (AOI) that reduces prototyping time and production costs by detecting defects early in the production process. Traditional defect detection method of human visual inspection is not only error prone but is also time-consuming given the growing complex and dense circuitry of modern-day electronics. Electric contact-based testing, either in the form of a bed of nails testing fixture or a flying probe system, is costly for low-rate rapid prototyping. An AOI is a non-contact test method using an image processing algorithm that quickly detects and reports failures within the PCB layer based on the captured image. A low-cost AOI system has been created using commercial off-the-shelf components specifically for low-rate production prototyping testing allowing testing of varying layers or various electronic designs without additional setup cost. Once the AOI system is physically configured, the image processing defect detection algorithm compares the test image with a defect-free reference image or by a set of pre-defined rules generated through Electronic Design and Analysis software. Detected defects are then classified into two main categories: fatal and potential. Fatal defects lead to the board\u27s rejection, while potential defects alert the operator to determine if the board should be rejected or will still satisfy pre-defined prototyping criteria. The specifications of an imaging system, camera sensor, imaging lens, and illumination set-up used in the creation of the AOI were designed considering a test PCB article already in production. The algorithm utilized is based on a non-reference defect detection method utilizing mathematical morphology-based image processing techniques to detect defects in the PCB under test

Persistent homology of time-dependent functional networks constructed from coupled time series

We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results. Our first example uses time-series output from networks of coupled Kuramoto oscillators. Our second example consists of biological data in the form of functional magnetic resonance imaging (fMRI) data that was acquired from human subjects during a simple motor-learning task in which subjects were monitored on three days in a five-day period. With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can sometimes play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used to distinguish between signal and noise. We find that persistent homology can detect differences in synchronization patterns in our data sets over time, giving insight both on changes in community structure in the networks and on increased synchronization between brain regions that form loops in a functional network during motor learning. For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops take place on the second of the three days of the learning process.Comment: 17 pages (+3 pages in Supplementary Information), 11 figures in many text (many with multiple parts) + others in SI, submitte

Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to create output summaries from our persistent-homology calculations, and we study the persistence landscapes and images using $k$-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their 1-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions